Earth Surface Systems

I Introduction.- 1 Systems and Models.- 1.1 Defining Systems.- 1.1.1 Systems as Form and Process Structures.- 1.1.2 Systems as Simple and Complex Structures.- 1.1.3 Systems and Their Surroundings.- 1.1.4 A Problem of Scale.- 1.2 Models of Systems.- 1.2.1 Conceptual Models.- 1.2.2 Scale Models.- 1.2.3 Mathematical Models.- II Conceptual Models.- 2 Simple and Complex Systems.- 2.1 Simple Systems.- 2.2 Systems of Complex Disorder.- 2.2.1 Irreversible Processes.- 2.2.2 Accounting Models: the Laws of Thermodynamics.- 2.3 Systems of Complex Order.- 2.3.1 Nonequilibrium Systems.- 2.3.2 Systems Far from Equilibrium.- 2.3.3 Open Systems at the Earth's Surface.- 3 Form and Process Systems.- 3.1 Models of System Form.- 3.1.1 Models of System Constitution.- 3.1.2 Models of System Geometry.- 3.2 Models of System Process.- 3.2.1 Land-Surface Cascades.- 3.2.2 Solid-Phase and Liquid-Phase Cascades.- 3.3 Models of System Form and Process.- 3.3.1 Concepts of Landscape Development.- 3.3.2 Concepts of Soil Development.- 3.3.3 Concepts of Soil-Landscape Development.- III Mathematical Models.- 4 Deductive Stochastic Models.- 4.1 Introduction to Probability.- 4.1.1 The Classical View of Probability.- 4.1.2 The Relative Frequency View of Probability.- 4.1.3 Axioms of Probability Theory.- 4.2 Independent Events in Time.- 4.2.1 Binomial Processes.- 4.2.2 Poisson Processes.- 4.3 Independent Events in Space.- 4.3.1 Point Patterns.- 4.3.2 Line Patterns.- 4.3.3 Area Patterns.- 4.4 Random-Walk Models.- 4.4.1 Stream Networks.- 4.4.2 Alluvial Fans.- 4.5 Markov Chains.- 4.5.1 Transition Probabilities.- 4.5.2 Sedimentary Sequences.- 4.5.3 Volcanic Activity.- 4.6 Entropy Models.- 4.6.1 Entropy Maximization.- 4.6.2 Entropy Minimization.- 4.6.3 Developments of the Thermodynamic Approach.- 5 Inductive Stochastic Models.- 5.1 Box and Jenkins's Models: an Introduction.- 5.1.1 System Definition.- 5.1.2 Stages in Systems Analysis.- 5.2 Autoregressive Moving-Average Models of Time Series.- 5.2.1 Model Formulation.- 5.2.2 Modelling Procedures.- 5.2.3 The Lagan Rainfall Series.- 5.3 Autoregressive Moving-Average Models of Distance Series.- 5.3.1 Model Formulation.- 5.3.2 River Meanders.- 5.3.3 Landforms.- 5.4 Transfer Function Models.- 5.4.1 Model Formulation.- 5.4.2 Rainfall and Runoff in the Lagan Drainage Basin.- 5.4.3 Channel Form in the Afon Elan, Wales.- 5.5 Problems of Inductive Stochastic Modelling.- 6 Statistical Models.- 6.1 Simple Regression and Correlation.- 6.1.1 The Regression Line.- 6.1.2 The Correlation Coefficient.- 6.1.3 Problems of Correlation.- 6.1.4 Linear Relations.- 6.1.5 Linear Versus Nonlinear Relations.- 6.2 Multiple Regression.- 6.2.1 "Simple" Multiple Regression.- 6.2.2 Trend Surface Analysis.- 6.2.3 Stepwise Regression.- 6.2.4 Problems of Multiple Regression.- 6.3 Correlation Systems.- 6.3.1 Principal Component Analysis.- 6.3.2 Principal Coordinate Analysis.- 6.3.3 Factor Analysis.- 6.3.4 Canonical Correlation.- 6.3.5 Problems with Correlation Systems.- 7 Deterministic Models of Water and Solutes.- 7.1 Ice.- 7.1.1 Glaciers.- 7.1.2 Ice Sheets.- 7.2 Water.- 7.2.1 Overland Flow.- 7.2.2 Open Channel Flow.- 7.2.3 Flow in Porous Media.- 7.2.4 Unsaturated Flow.- 7.3 Solutes.- 7.3.1 Seas and Lakes.- 7.3.2 Solutes in Groundwater.- 7.3.3 Solutes in Soils.- 8 Deterministic Models of Slopes and Sediments.- 8.1 Discrete Component Models.- 8.2 Analytical Models.- 8.2.1 Heuristic Models.- 8.2.2 Models Based on the Continuity Equation.- 8.3 Simulation Models.- 8.3.1 Landscape Simulation.- 8.3.2 Drainage Basin Simulation.- 8.3.3 Nearshore Bar Formation.- 8.3.4 Sand Dune Formation.- 9 Dynamical Systems Models.- 9.1 Model Building.- 9.1.1 State and State Change.- 9.1.2 Transfer Equations.- 9.2 System Stability.- 9.2.1 State Space.- 9.2.2 Sensitivity Analysis.- 9.3 Biogeochemical Cycles.- 9.3.1 The Global Cycle of Phosphorus.- 9.3.2 The Global Cycle of Carbon Dioxide and Oxygen.- 9.3.3 Strontium and Manganese in a Tropical Rain Forest.- 9.3.4 Water in Soils.- 9.3.5 Nutrients in Lake Erie.- 9.4 Dissipative Structures.- 9.4.1 Bifurcations and Catastrophes.- 9.4.2 Thresholds.- 9.4.3 Dominance Domains.- 10 Conclusion and Prospect.- 10.1 Models as a Complement to Field Studies.- 10.2 Models as a Testing Ground for Long-Term Change.- 10.3 Models as Good Predictors of Complex Situations.- References.